## Absolutely continuous spectrum of a typical Schrödinger operator with a slowly decaying potential    [PDF]

Oleg Safronov
We consider a family of multi-dimensional Schr\"odinger operators $-\Delta+t V$ with a real $t$. The potential $V$ in our model decays at infinity in a special way, so that it satisfies a certain integral condition. We prove that the absolutely continuous spectrum of this operator covers the interval $[0,\infty)$ for almost every $t$.
View original: http://arxiv.org/abs/1111.5552